diff --git a/bytesconv.go b/bytesconv.go
index 5f39dcc..13ce724 100644
--- a/bytesconv.go
+++ b/bytesconv.go
@@ -8,6 +8,7 @@ import (
 	"io"
 	"math"
 	"net"
+	"reflect"
 	"sync"
 	"time"
 	"unsafe"
@@ -360,6 +361,20 @@ func b2s(b []byte) string {
 	return *(*string)(unsafe.Pointer(&b))
 }
 
+// s2b converts string to a byte slice without memory allocation.
+//
+// Note it may break if string and/or slice header will change
+// in the future go versions.
+func s2b(s string) []byte {
+	sh := (*reflect.StringHeader)(unsafe.Pointer(&s))
+	bh := reflect.SliceHeader{
+		Data: sh.Data,
+		Len:  sh.Len,
+		Cap:  sh.Len,
+	}
+	return *(*[]byte)(unsafe.Pointer(&bh))
+}
+
 // AppendQuotedArg appends url-encoded src to dst and returns appended dst.
 func AppendQuotedArg(dst, src []byte) []byte {
 	for _, c := range src {
diff --git a/uri.go b/uri.go
index 6249f44..684b8f9 100644
--- a/uri.go
+++ b/uri.go
@@ -286,8 +286,19 @@ func normalizePath(dst, src []byte) []byte {
 	}
 	dst = dst[:bSize]
 
-	// remove /foo/../ parts
+	// remove /./ parts
 	b = dst
+	for {
+		n := bytes.Index(b, strSlashDotSlash)
+		if n < 0 {
+			break
+		}
+		nn := n + len(strSlashDotSlash) - 1
+		copy(b[n:], b[nn:])
+		b = b[:len(b)-nn+n]
+	}
+
+	// remove /foo/../ parts
 	for {
 		n := bytes.Index(b, strSlashDotDotSlash)
 		if n < 0 {
@@ -302,17 +313,6 @@ func normalizePath(dst, src []byte) []byte {
 		b = b[:len(b)-n+nn]
 	}
 
-	// remove /./ parts
-	for {
-		n := bytes.Index(b, strSlashDotSlash)
-		if n < 0 {
-			break
-		}
-		nn := n + len(strSlashDotSlash) - 1
-		copy(b[n:], b[nn:])
-		b = b[:len(b)-nn+n]
-	}
-
 	// remove trailing /foo/..
 	n := bytes.LastIndex(b, strSlashDotDot)
 	if n >= 0 && n+len(strSlashDotDot) == len(b) {
@@ -371,8 +371,7 @@ func (u *URI) LastPathSegment() []byte {
 //     * Relative path, i.e.  xx?yy=abc . In this case the original RequestURI
 //       is updated according to the new relative path.
 func (u *URI) Update(newURI string) {
-	u.fullURI = append(u.fullURI[:0], newURI...)
-	u.UpdateBytes(u.fullURI)
+	u.UpdateBytes(s2b(newURI))
 }
 
 // UpdateBytes updates uri.
@@ -409,22 +408,28 @@ func (u *URI) updateBytes(newURI, buf []byte) []byte {
 	}
 
 	// relative path
-	if newURI[0] == '?' {
+	switch newURI[0] {
+	case '?':
 		// query string only update
 		u.SetQueryStringBytes(newURI[1:])
+		return append(buf[:0], u.FullURI()...)
+	case '#':
+		// update only hash
+		u.SetHashBytes(newURI[1:])
+		return append(buf[:0], u.FullURI()...)
+	default:
+		// update the last path part after the slash
+		path := u.Path()
+		n = bytes.LastIndexByte(path, '/')
+		if n < 0 {
+			panic("BUG: path must contain at least one slash")
+		}
+		buf = u.appendSchemeHost(buf[:0])
+		buf = appendQuotedPath(buf, path[:n+1])
+		buf = append(buf, newURI...)
+		u.Parse(nil, buf)
 		return buf
 	}
-
-	path := u.Path()
-	n = bytes.LastIndexByte(path, '/')
-	if n < 0 {
-		panic("BUG: path must contain at least one slash")
-	}
-	buf = u.appendSchemeHost(buf[:0])
-	buf = appendQuotedPath(buf, path[:n+1])
-	buf = append(buf, newURI...)
-	u.Parse(nil, buf)
-	return buf
 }
 
 // FullURI returns full uri in the form {Scheme}://{Host}{RequestURI}#{Hash}.
diff --git a/uri_test.go b/uri_test.go
index 3e519dc..508a9ba 100644
--- a/uri_test.go
+++ b/uri_test.go
@@ -109,6 +109,9 @@ func TestURIUpdate(t *testing.T) {
 	testURIUpdate(t, "http://foo.bar/baz", "~a/%20b=c,тест?йцу=ке", "http://foo.bar/~a/%20b=c,%D1%82%D0%B5%D1%81%D1%82?йцу=ке")
 	testURIUpdate(t, "http://foo.bar/baz", "/qwe#fragment", "http://foo.bar/qwe#fragment")
 	testURIUpdate(t, "http://foobar/baz/xxx", "aaa.html#bb?cc=dd&ee=dfd", "http://foobar/baz/aaa.html#bb?cc=dd&ee=dfd")
+
+	// hash
+	testURIUpdate(t, "http://foo.bar/baz#aaa", "#fragment", "http://foo.bar/baz#fragment")
 }
 
 func testURIUpdate(t *testing.T, base, update, result string) {
@@ -166,6 +169,7 @@ func TestURIPathNormalize(t *testing.T) {
 	testURIPathNormalize(t, &u, "/a/./b/././c/./d.html", "/a/b/c/d.html")
 	testURIPathNormalize(t, &u, "./foo/", "/foo/")
 	testURIPathNormalize(t, &u, "./../.././../../aaa/bbb/../../../././../", "/")
+	testURIPathNormalize(t, &u, "./a/./.././../b/./foo.html", "/b/foo.html")
 }
 
 func testURIPathNormalize(t *testing.T, u *URI, requestURI, expectedPath string) {